I don’t have a huge amount of evidence for this, but Varys and Illyrio share a bond of trust and partnership that has endured for decades and across oceans, which is pretty rare in ASOIAF. 

So one of the things that struck me in Tyrion I of ADWD is this passage that comes immediately after Tyrion meets Illyrio as a “friend of Varys the Spider”:

Beneath his window six cherry trees stood sentinel around a marble pool, their slender branches bare and brown. A naked boy stood on the water, poised to duel with a bravo’s blade in hand. He was lithe and handsome, no older than sixteen, with straight blond hair that brushed his shoulders. So lifelike did he seem that it took the dwarf a long moment to realize he was made of painted marble, though his sword shimmered like true steel.

And then in Tyrion II we get this exchange that gives context to what it represents:

“…even fat old fools like me have friends, and debts of affection to repay.”

“…How is it that the Spider became so dear to you?“

“We were young together, two green boys in Pentos.”

“Varys came from Myr.”

“So he did. I met him not long after he arrived, one step ahead of the slavers. By day he slept in the sewers, by night he prowled the rooftops like a cat. I was near as poor, a bravo in soiled silks, living by my blade. Perhaps you chanced to glimpse the statue by my pool? Pytho Malanon carved that when I was six-and-ten. A lovely thing, though now I weep to see it.”

“Age makes ruins of us all. I am still in mourning for my nose. But Varys …”

“In Myr he was a prince of thieves, until a rival thief informed on him. In Pentos his accent marked him, and once he was known for a eunuch he was despised and beaten. Why he chose me to protect him I may never know, but we came to an arrangement. Varys spied on lesser thieves and took their takings. I offered my help to their victims, promising to recover their valuables for a fee. Soon every man who had suffered a loss knew to come to me, whilst city’s footpads and cutpurses sought out Varys … half to slit his throat, the other half to sell him what they’d stolen. We both grew rich, and richer still when Varys trained his mice.”

I found it interesting that the symbol of Illyrio’s past is a depiction of male beauty – clearly, back in the day, Illyrio was enough of a hottie to inspire sculptors to work pro-bono, since he was only “a bravo in spoiled silks” back then. And Illyrio thinks of Varys’ “dearness” as associated with that youthful beauty, of being youths together. 

(credit to Pojypojy)

Now, it’s could all be totally platonic, but it’s not like there isn’t a history of homosocial and homoromantic relationships between young men in Renaissance city-states. And there’s something about the way that Illyrio says “why he chose me to protect him I may never know” that reminds me of people in long-term relationships who talk about not knowing what their partner saw in them in the beginning. 

And if we’re going by the usual GRRM metrics of what would the most tragic possible outcome be, imagine this scenario. Varys and Illyrio are lovers, and trust each other implicitly. Indeed, so self-sacrificing is Varys that he elevates Illyrio to wealth and power to the point where Illyrio gets married to the Prince’s cousin, and Varys even overlooks Illyrio’s passion for Sera. 

But then Varys executes the greatest scheme in their careers, the one that actually means something to him because of the possibility of producing the perfect prince,  and he gives over the royal baby he smuggled out of King’s Landing into the hands of the one person he trusts in the world. And Illyrio, out of love for the other woman, replaces that baby with his own son. What more profound betrayal can you imagine?